Mathematical representation has an essential role in solving mathematical problems. However, there are still many mathematics education students who have difficulty in representing ill-structured problems. Even though the ill-structured-problem-solving tasks designed to help mathematics education students understand the relevance and meaningfulness of what they learn, they also are connected with their prior knowledge. The focus of this research is exploring the used of mathematical representations in solving ill-structured problems involving quadratic functions. The topic of quadratic functions is considered necessary in mathematics teaching and learning in higher education. It's because many mathematics education students have difficulty in understanding these matters, and they also didn’t appreciate their advantage and application in daily life. The researchers' explored mathematical representation as used by two subjects from fifty-four mathematics education students at the University of Nusantara PGRI Kediri by using a qualitative approach. We were selected due to their completed all steps for solving the ill-structured problem, and there have different ways of solving these problems. Mathematical representation explored through an analytical framework of solving ill-structured issues such as representing problems, developing alternative solutions, creating solution justifications, monitoring, and evaluating. The data analysis used technique triangulation. The results show that verbal and symbolic representations used both subjects to calculate, detect, correct errors, and justify their answers. However, the visual representation used only by the first subject to detect and correct errors.

Salah satu yang menjadi alasan kesulitan siswa kurang dapat memecahkan masalah matematika adalah kurangnya ragam representasi yang dimiliki siswa. Oleh karena itu representasi penting dalam suatu pembelajaran matematika. Kurangnya kemampuan representasi siswa terlihat ketika siswa kesulitan menggunakan representasinya untuk memecahkan permasalahan aplikasi turunan fungsi. Adapun perbedaan representasi siswa dalam memecahkan masalah tersebut juga dipengaruhi oleh gaya kognitif siswa tersebut. Untuk itu dilakukan suatu penelitian kualitatif yang bertujuan mendeskripsikan: (1) representasi siswa SMA dengan gaya kognitif Field Dependent dalam memecahkan masalah matematika (2) representasi siswa SMA dengan gaya kognitif Field Independent dalam memecahkan masalah matematika. Pengumpulan data dilakukan dengan pemberian tugas TPMO dan wawancara. Teknik pemeriksaan keabsahan data yang digunakan adalah triangulasi. Subjek penelitian adalah siswa SMA kelas XII sebanyak 2 orang. Hasil penelitian ini menunjukkan bahwa subjek mereprentasikan idenya untuk memecahkan masalah matematika dengan menggunakan langkah pemecahan masalah Polya: (a) memahami masalah (b) membuat rencana penyelesaian (c) melaksanakan rencana dan (d) memeriksa kembali penyelesaian yang telah dilakukan. Adapun representasi subjek dengan gaya kognitif Field Dependent dalam memecahkan masalah matematika adalah dengan cara: memahami informasi dan apa yang ditanyakan dengan membuat gambar, membuat rencana penyelesaian dengan membuat persamaan matematika, memanipulasi persamaan tersebut dan mengecek kembali hasil akhir yang didapatkan dengan mensubstitusi kembali jawaban akhir ke persamaan awal. Sedangkan subjek dengan gaya kognitif Field Independent merepresentasikan idenya untuk memecahkan masalah dengan cara: memahami informasi dan apa yang ditanyakan dengan menuliskan persamaan matematika menggunkan simbol formal, membuat rencana penyelesaian dengan membuat persamaan matematika, memanipulasi persamaan tersebut dan menggunakan cara coba-coba serta tidak melakukan pengecekan kembali hasil akhir yang diperoleh.

Penelitian ini dilatarbelakangi rendahnya hasil PISA dan TIMSS siswa Indonesia yang kontradiktif dengan motivasi belajar mereka. Untuk itu dilakukan penelitian dengan tujuan untuk mendeskripsikan kemampuan literasi matematis siswa SMP dengan tingkat motivasi belajar rendah dan tinggi. Identifikasi kemampuan literasi matematis didasarkan atas indikator literasi matematis yang meliputi: komunikasi, matematisasi, representasi, pemilihan strategi untuk pemecahan masalah, serta penalaran. Subjek penelitian terdiri dari 1 siswa untuk masing-masing kategori. Instrumen penelitian meliputi peneliti, tes literasi matematis, angket motivasi belajar siswa, dan pedoman wawancara. Teknik pengumpulan data yang digunakan terdiri dari tes, wawancara, dan observasi. Teknik analisis data menggunakan triangulasi teknik. Analisis data dilakukan dengan cara reduksi data, penyajian data, dan pengambilan simpulan. Adapun hasil penelitian menyatakan bahwa kemampuan literasi matematis siswa motivasi belajar rendah dan rendah memiliki kesamaan dalam komunikasi dan matematisasi. Sedangkan pada saat pemilihan strategi pemecahan masalah, representasi dan penalaran terdapat perbedaan antara kedua subjek. Perbedaan tersebut terletak pada cara yang dipilih siswa dengan motivasi belajar tinggi dalam melihat fokus permasalahan dan menganalisa jawaban, sedangkan siswa dengan motivasi belajar rendah lebih memilih cara prosedural.Kata kunci: Literasi Matematis, Siswa SMP, Motivasi Belajar

PENDAHULUAN Menurut Hix (2008) "Lesson study is a Japanese model of professional development in which teachers collaboratively plan and study live lessons";artinya lesson study salah satu model pembinaan profesi pendidik melalui pengkajian pembelajaran secara kolaboratif dan berkelanjutan. Dalam kolaboratif termuat prinsip kolaborasi saling membantu untuk membangun komunitas belajar.Lesson study bukan sebuah proyek sesaat, tetapi merupakan kegiatan terus menerus yang tiada henti dan merupakan sebuah upaya untuk mengaplikasikan AbstractLesson study is one model of professional guidance for educators that are relevant to the need for increased learning support skills (soft skill) teachers. The improvement of soft skill can be developed by learning critical. This research proposes to describe (1) improving soft skill of mathematics students through the implementation of lesson study, and (2) increasing the student activities in the learning phase criting after the application of lesson study. This research is a descriptive research, this research explains the increase in soft skill and elements of criting FRISCO (Focus, Reason, Inference, Situation, Clarity, Overview) in the learning phase of criting lesson study. Sampling technique used is purposive sampling. The research subjects are the students of mathematics education who took the course MKPBM 4. The data was collected through observation. The research steps begin with plan, do and see between model (researcher) and the observer. The result of this study indicates that the lesson study provides positive contribution in learning process. It can be seen from the increase in soft skill of students who reach the final average of 2.18 (on a moderate), and critical thinking skill reaches an average of 2.35 (on a high level). The contribution creates an openness in learning for all sides. A class which has an openness to all people will have a positive impact for the model, students, and observer.

<p>Mathematical representation is an essential aspect of mathematical problem-solving. But students’ ability of an accurate representation in ill-posed problem-solving is still very minimal compared to that in well-posed problem-solving. However, ill-posed problem supported mathematical abstraction used in mathematical concept understanding. This study described the representations used by mathematics education students in solving ill-posed and well-posed problems. Thirty Indonesian matematics education students have solved ill-well posed problems by using think-aloud. Researchers also collected data using a video recorder and a field note. Data were analyzed by a constant comparative method so that it was obtained the different characteristics of representations between solving ill-posed and well-posed problems. The finding of the study showed that verbal and symbolic representations were used by subjects to compute, detect, and correct error. They also justified their answers in ill-posed problem-solving. However, the visual representation was only used by first subject to identify and correct error. The subjects lacked to expose necessary information to solve the ill-posed problem compared to the well-posed problem.</p>